To Diagonalize an n × n Matrix, A . . . 1. Find all eigenvalues with their algebraic multiplicities. To do this, solve the equation det( A-λI ) = 0 for λ . 2. For each eigenvalue, λ , ﬁnd the corresponding eigenspace, E λ = ker( A-λI ). The dimension of E λ is the geometric multiplicity of λ . 3. If the geometric multiplicity of each eigenvalue is the same as its algebraic multiplic-ity, or equivalently, if the geometric multiplicities add up to n , then the matrix is diagonalizable. 4. If the matrix is diagonalizable, collect together the bases of each eigenspace. The

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